In a party, 75 persons took tea, 60 persons took coffee and 15 persons took both tea and coffee. No one taking milk takes tea. Each person takes at least one drink. Question : How many persons attended the party ? Statement-1 : 50 persons took milk. Statement-2 : Number of persons who attended the party is five times the number of persons who took milk only. Which one of the following is correct in respect of the above Question and the Statements ?
- (a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone. ✓ UPSC's answer
- (b) The Question can be answered by using either Statement alone.
- (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
- (d) The Question cannot be answered even by using both the Statements together.
Why the answer is (a)
• From the given data, tea drinkers = 75, coffee drinkers = 60, and tea ∩ coffee = 15, so the number of people who take tea or coffee (or both) is 75 + 60 − 15 = 120. Since no one taking milk takes tea, every milk drinker lies entirely outside the tea set, meaning milk drinkers can only be among the 45 people who take coffee but not tea, or among those who take milk alone.
• Let x = number of people who take both coffee and milk (but not tea), and y = number of people who take milk only. The total number of attendees is then 60 (tea only) + (45 − x) (coffee only, no milk) + 15 (tea and coffee) + x (coffee and milk) + y (milk only) = 120 + y.
• Statement 1 tells us M = x + y = 50, so Total = 120 + y = 120 + (50 − x) = 170 − x. Because x can range from 0 to 45, the total is not uniquely determined; Statement 1 alone is insufficient.
• Statement 2 states that Total = 5 × (milk only) = 5y. Substituting into Total = 120 + y gives 5y = 120 + y, so 4y = 120, y = 30, and Total = 5 × 30 = 150. Statement 2 alone is sufficient.
• Since Statement 2 alone yields a unique answer (150) while Statement 1 alone does not, the correct choice is (a): the question can be answered by one statement alone but not by the other.
Why the other options are wrong
- (b) The Question can be answered by using either Statement alone.
- Statement 1 gives M = 50 but leaves x (coffee-and-milk drinkers) undetermined, so the total cannot be pinned down from Statement 1 alone; only Statement 2 is sufficient, not both.
- (c) The Question can be answered by using both the Statements together, but cannot be…
- Statement 2 by itself produces a unique value (Total = 150) without any need for Statement 1, so the two statements are not jointly required.
- (d) The Question cannot be answered even by using both the Statements together.
- Statement 2 alone is sufficient to compute the total as 150, so the question is answerable; it is not the case that even both statements together fail.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2023, held on 28 May 2023. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.